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In this work we directly fit the QCD dimensional transmutation parameter,${\Lambda _{\overline {MS} }}$, to experimental data of Drell-Yan (DY)observables. For this purpose we first obtain the evolution of transversemomentum dependent parton distribution functions (TMDPDFs) up to the NNLOapproximation based on Collins-Sopper-Sterman formalism. As is expecting theTMDPDFs are appearing at larger values of transvers momentum by increasing theenergy scales and also the order of approximation. Then we calculate the crosssection related to the TMDPDFs in the DY process. As a consequence of fittingto the E288 experimental data at center of mass energy $\sqrt{s}=23.8$ $GeV$,we obtain ${\Lambda _{\overline {MS} }} = 249 \pm 7 MeV$ corresponding to therenormalized coupling constant ${\alpha _s}(M_z^2) = 0.119 \pm 0.001$ which iswithin the acceptable range for this quantity. The results for DY cross sectionat different energy scales are in good agreement within the available data.

Extracting the QCD ${\Lambda _{\overline {MS} }}$ parameter in Drell-Yan Process using Collins-Sopper-Sterman approach